期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 21, 期 3, 页码 515-539出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202511005131
关键词
Kinetic theory; measure solutions; interacting particle systems; Monge-Kantorovich-Rubinstein distance; stability; particle methods; swarming
资金
- DGI-MCI (Spain) [MTM2008-06349-C03-03]
- AGAUR-Generalitat de Catalunya [2009-SGR-345]
We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the behavior of large groups of animals, such as flocks of birds, swarms, or schools of fish. Our aim is to give a well-posedness theory for general models which possibly include a variety of erects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging erect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and self-propulsion erects,which take into account erects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory, we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models.
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